SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS

Abstract

A criterion for a simple object of the representation category $\Rep(D^\omega(G))$ of the twisted Drinfeld double $D^\omega(G)$ to be a generator is given, where $G$ is a finite group and $\omega$ is a 3-cocycle on $G$. A description of the adjoint category of $\Rep(D^\omega(G))$ is also given.